The present invention relates generally to code tracking and/or carrier tracking a broadcast signal contained in a spread-spectrum signal.
A CDMA telephony system is based on spread-spectrum technology and is one of the most widely used digital wireless services today. The spread-spectrum signal requires sophisticated broadcast power management and soft hand-overs between base stations. This means that the base stations must be precisely timed. With the CDMA wireless telephony system, each transmitter must maintain its frequency to within one part in ten billions. Currently, GPS technology enables accurate timing and synchronization between base stations so that cellular calls can be flawlessly passed from one base station to another.
The GPS satellites transmit two microwave carrier signals: the L1 frequency (1575.42 MHz) which carries the navigation message and the Standard Positioning Services (SPS) code signals; and the L2 frequency (1227.60 MHz) which is used for ionospheric delay measurement carried out by the Precise Positioning Services (PPS) equipped receivers. Three binary codes are used to shift the L1 and/or L2 carrier phases: 1) the Coarse Acquisition (C/A) Code, which is a repeating 1.023 MHz Pseudo Random Noise (PRN), code-modulates the L1 carrier phase, spreading the spectrum over a 2.046 MHz bandwidth. For the code-phase modulation, each GPS satellite is assigned a different C/A code PRN, so that each GPS satellite can be identified by a unique PRN code; 2) the Precise (P) Code uses a 10.23 MHz PRN code for modulating both the L1 and L2 carrier phases for the military receivers; and 3) the navigation message, which is used to modulate the L1-C/A or P(Y) code signal, is a 50 Hz signal consisting of data bits that describe the GPS satellite orbits, system time, position, clock corrections, and other system parameters. The position of a certain satellite at a given time is provided by the ephemeris information, which is based on a list of accurate positions or locations of a celestial object as a function of time, available as xe2x80x9cbroadcast ephemerisxe2x80x9d or as post-processed xe2x80x9cprecise ephemerisxe2x80x9d.
Signals from the GPS satellites are subject to electromagnetic interference, or EMI. Microwave signals also suffer from absorption and/or scattering by water vapor, massive downpours, dark cloud cover, and man-made and natural obstacles. Therefore, the CDMA signal in a GPS receiver can be very weak and noisy. In telephony applications, it is essential that the CDMA signals be tracked and locked at all times during a telephone connection.
The present invention provides a method, system and device to lock in and track a weak and noisy CDMA signal streaming in a GPS receiver. However, the present invention can also be applied to tracking a weak and noisy broadcast signal in any spread-spectrum signal. In particular, the spread-spectrum signal contains a unique PRN for code phase modulation and a known carrier frequency.
The method, system and device, according to the present invention, uses an adaptive and time-variant digital filter in the code or carrier tracking loop of the spread spectrum receiver for signal extraction. More specifically, the adaptive and time-variant digital filter is based on the AutoRegressive (AR) model described by a difference equation, computed according to the Maximum Entropy Method (MEM) recursion algorithm as devised by J. P. Burg.
The loop filter used in the spread spectrum receiver or the GPS receiver, according to the present invention, is based on the AR model of the process described by a linear equation as follows:
x(t)=a1x(txe2x88x921)+a2x(txe2x88x922)+ . . . +aMx(txe2x88x92M)+n(t)
where x(t) is an observed or new value of the time series; ak""s are the coefficients to be determined; x(txe2x88x92k) is a known time series; M is the degree of the autoregressive process, and n(t) is an input signal to a system that generates a predicted value of x(t). For example, n(t) can be samples of a Gaussian noise varying with time.
The open loop transfer function of the loop filter as described above is the time series spectrum, represented by the z-transform:
xe2x80x83F(z)=1/(1xe2x88x92a1zxe2x88x921xe2x88x92a2zxe2x88x922xe2x88x92 . . . xe2x88x92aMzxe2x88x92M)
where zxe2x88x921 is a delay time unit.
The loop filter must have sufficient memory for storing a plurality of values of the time series so that it can be used to predict the time series ahead of as many values as desired. The major task here is to compute the values of ak. According to the present invention, the coefficients ak are computed by the Maximum Entropy Method (MEM) which is based on the idea to maximize the entropy of the time series x(t). In that respect, the loop filter is a matched filter. In such a matched filter, the computation is based on the information of the signal contained in the time series x(t), and not on the physical characteristics of the signal. The time series will provide the maximum amount of information for the filtering system.
As is well known in the Information Theory, entropy is defined by:   H  =      -                  ∫                  -          ∞                ∞            ⁢                        p          ⁡                      (            x            )                          ⁢                  xe2x80x83                ⁢                              log            2                    ⁡                      (                          p              ⁡                              (                x                )                                      )                          ⁢                  ⅆ          x                    
where p(x) is the probability associated with the value of x in an involved process.
Some restrictions must be made when maximizing the entropy. Assuming that the process is almost or entirely stationary, the entropy can be maximized under the restriction of the following two conditions:             ∫              -        ∞            ∞        ⁢                  p        ⁡                  (          x          )                    ⁢              xe2x80x83            ⁢              ⅆ        x              =  1
and             ∫              -        ∞            ∞        ⁢                  p        ⁡                  (          x          )                    ⁢              xe2x80x83            ⁢              x        2            ⁢              ⅆ        x              =      σ    2  
where "sgr"2 is equal to the power of the signal and is a constant.
With the restrictions in place, the entropy is maximized by dH/dt=0. In practice, the maximization can be realized by the Burg""s recursion algorithm or any other recursive numerical algorithm. A discussion on the Burg""s Maximum Entropy Algorithm can also be found in D. E. Smylie, G. K. C. Clark and T. J. Ulrych xe2x80x9cAnalysis of Irregularities in the Earth""s Rotationxe2x80x9d (METHODS IN COMPUTATIONAL PHYSICS, VOL 13, pp. 391-430, Academic, New York, 1973). A representative autoregressive algorithm can be found in L. Marple xe2x80x9cA New Autoregressive Spectrum Analysis Algorithmxe2x80x9d (IEEE TRANSACTIONS ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING, VOL. ASSP-28, NO.4, AUGUST 1980). The following analysis is based on the approach as disclosed in J. Mannermaa and M. Karras xe2x80x9cUse of the Maximum Entropy Method to Predict Atmospheric CO2 Contentxe2x80x9d (GEOPHYSICA , 25, 1and2, 37-46, 1989).
First, the output power of the times series S1 is estimated after the digital filter order of one (1, a11). The filter is operated in the time series both forward and backward. Accordingly, S1 can be expressed as       S    1    =      (                  ∑                  t          =          1                          N          -          1                    ⁢                                    (                                                            (                                                            x                      t                                        -                                                                  a                        11                                            ⁢                                              x                                                  t                          +                          1                                                                                                      )                                2                            +                                                (                                                            x                                              t                        +                        1                                                              -                                                                  a                        11                                            ⁢                                              x                        t                                                                              )                                2                                      )                    /                      (                          N              -              1                        )                          /        2            
Minimizing S1 as a function of a11 gives       a    11    =      2    ·                  ∑                  t          =          1                          N          -          1                    ⁢                        (                                    x              t                        ·                          x                              t                +                1                                              )                /                              ∑                          t              =              1                                      N              -              1                                ⁢                      (                                          x                                  t                  +                  1                                2                            +                              x                t                2                                      )                              
In general, the length of the filter (m) is increased and the corresponding powers Sm are estimated such that       S    m    =                    {                              ∑                          t              =              1                                      N              -              m                                ⁢                      (                                                            (                                                            x                      t                                        -                                                                  ∑                                                  u                          =                          1                                                m                                            ⁢                                                                        a                          mu                                                ⁢                                                  x                                                      t                            +                            u                                                                                                                                )                                2                            +                                                (                                                            x                                              t                        +                        m                                                              -                                                                  ∑                                                  u                          =                          1                                                m                                            ⁢                                                                        a                          mu                                                ⁢                                                  x                                                      t                            +                            m                            -                            u                                                                                                                                )                                2                                      )                          }            /              (                  N          -          m                )              /    2  
It has been known that
amu=amxe2x88x921uxe2x88x92ammxc2x7amxe2x88x921mxe2x88x92u
where
m=2,3, . . . , Nxe2x88x921
u=1,2, . . . , mxe2x88x921
am0=xe2x88x921
amu=0 for uxe2x89xa7m
By using the formulae of Sm and amu and xcex4Sm/xcex4amm=0, the general term amm can be solved and presented in the following form       a    mm    =      2    ·                  ∑                  u          =          1                          N          -          m                    ⁢                        (                      B            ⁢                          xe2x80x83                        ⁢                                          A                mu                            ·              B                        ⁢                          xe2x80x83                        ⁢                          B              mu                                )                /                              ∑                          u              =              1                                      N              -              m                                ⁢                      (                                          B                ⁢                                  xe2x80x83                                ⁢                                  A                  mu                  2                                            +                              B                ⁢                                  xe2x80x83                                ⁢                                  B                  mu                  2                                                      )                              
where
BAmu=BAmxe2x88x921uxe2x88x92amxe2x88x921 mxe2x88x921xc2x7BBmxe2x88x921mxe2x88x92u 
BBmu =BBmxe2x88x921u+1xe2x88x92amxe2x88x921mxe2x88x921xc2x7BAmxe2x88x921u+1 
m=2,3, . . . , M
u=1,2, . . . , Nxe2x88x92m
BA1u=x(t)
BB1u=x(t+1)
The digital filter (1, xe2x88x92a11, . . . , amm) for implementing the above algorithm is normally presented in the form of (1, xe2x88x92a1, . . . , aM). Such a filter is generally known as the prediction error filter. When this digital filter is used in a spread spectrum or GPS receiver, the coefficients ak are updated right after every pre-integration sequence. The prediction error filter as described above is shown in FIG. 3.
The first aspect of the present invention is to provide a system and device for code and/or carrier tracking a broadcast signal contained in a spread spectrum signal, wherein the spread spectrum signal includes a code signal and a carrier signal. The system comprises:
a receiver to receive the spread spectrum signal; and
a filtering circuit to process the received signal in order to code-phase tracking the broadcast signal, wherein the filtering circuit includes at least an adaptive and time variant digital filter.
In particular, the adaptive and time variant digital filter is based on an AutoRegressive (AR) model of a Maximum Entropy Method (MEM) algorithm, and wherein the broadcast signal may include a CDMA signal and the spread spectrum signal may include a GPS signal. The device may additionally comprise another filtering circuit to process the received signal for carrier-tracking the broadcast signal. Alternatively, another type of adaptive and time variant digital filters based on the Maximum Likelihood Method, Minimum Variance Method or a statistical signal filtering method is used in lieu of the Maximum Entropy Method.
The second aspect of the present invention is to provide a method of tracking a broadcast signal contained in a spread spectrum signal, wherein the spread spectrum signal contains a code signal and a carrier signal. The method comprises the steps of:
receiving the spread spectrum signal; and
processing the received signal through a filter circuit in order to extract the code signal for code-phase tracking the broadcast signal, wherein the filter circuit comprises an adaptive and time variant digital filter.
In particular, the adaptive and time variant digital filter is based on an AutoRegressive (AR) model of Maximum Entropy Method (MEM) algorithm, and wherein the broadcast signal may include a CDMA signal and the spread spectrum signal may include a GPS signal. Alternatively, another type of adaptive and time variant digital filters based on the Maximum Likelihood Method, Minimum Variance Method or a statistical signal filtering method is used in lieu of the Maximum Entropy Method.
The method may additionally comprise the step of filtering the received signal through the filter circuit for removing a Doppler signal in the carrier signal for carrier tracking the broadcast signal.
The present invention will become apparent upon reading the description taken in conjunction with FIGS. 1 to 3.